Although there are plenty of measurements on the Sivers asymmetry combined with phenomenological extractions, our knowledge on the Sivers function is still limited.
Currently, most of the information from theoretical study and data focuses on the Sivers functions of the valence quarks.
The Sivers functions of the sea quarks and gluon are less constrained compared to those of the \(u\)  and \(d\)  quarks.
In the Drell-Yan process, the anti-quarks play a more significant role since the dominant sub-process is \(q \bar{q}\rightarrow \gamma ^\star \rightarrow \) .
The time-reversal property of the Sivers function predicts that it present generalized universality, i.e., the sign of the Sivers function measured in Drell-Yan process should be opposite to its sign measured in SIDIS [1]}, [2]}, [3]}.
The verification of this sign change [4]}, [5]}, [6]}, [7]}, [8]} is one of the most fundamental tests of our understanding of the QCD dynamics, and it is also the main pursue of the existing and future Drell-Yan facilities [9]}, [10]}, [11]}.
As pointed out in Ref. [12]}, the sea quark Sivers function could play an important role in the test of the sign-change between SIDIS and Drell-Yan, since the sign for anti-quark Sivers function almost exclusively defines the sign of the asymmetry of Drell-Yan and \(W/Z\)  production in polarized \(p p\)  collision.
Furthermore, sea quark Sivers function is also of importance to explain the azimuthal asymmetry of kaon production in in SIDIS.
